To fully understand how culture works, it's important to first understand that there's a distinction between 'city culture' and 'plot culture'.
City culture is the number shown in the city screen. For each point of culture the city creates, with artists, buildings, or whatever, the city culture increases and you can see the precise increase by looking at the culture bar in the city screen.
Plot culture is a behind-the-scenes number which is used in various game mechanics, but is not directly displayed anywhere. Plot culture is what determines the cultural ownership of any particular plot. The plot culture on the city plot is not the same as the city culture in the city. Whenever city culture is created, some plot culture is also created on the city plot, and on all of the plots near the city. The specific formula of how much plot culture is created is the main thing that K-Mod has changed. In K-Mod, plot culture has a much stronger connection to city culture compared to the unmodded game; and is spread further. (In the unmodded game, the creation of culture in a city only produced relatively little plot culture; but in K-Mod, that's the primary way plot culture is created.)
Culture flipping has essentially nothing to do with city culture, and everything to do with plot culture. To flip the city, you must have significantly more plot culture on the city plot than the owner of the city; but the city culture is not important. In fact, you'll usually have 0 city culture when you flip the city.
Trade route culture is pretty unimportant really. The trade route culture listed in the city screen is applied to the plots around the city in the same way as it would coming from an artist or whatever, except for two things: Firstly, the culture belongs to the civilization of the trade city. Secondly, the culture does not add to the city culture. (Most sources of culture add to the city culture, and to plot culture. But this source only adds to plot culture.)
The point of trade culture is that I wanted the cultural influence of civilizations to spread across the whole world, rather than just spread to their immediate borders. When I first implemented it, it did contribute to city culture; but after trying various formulas and changes to try to get the balance right, I decided it was impossible to get a noticeable affect on city ownership without having a huge effect on cultural victory strategies... so I changed it to be plot-culture only.
The spread culture espionage mission adds to both city culture and to plot culture. It's essentially the same as a mini-culture bomb from a great artist. (Actually, I'm considering changing the espionage mission so that it does not add to city culture - because I think it's a bit weird, and because it could lead to a kind of 'exploit' in multiplayer games where players cooperate to get a cultural victory by doing lots of spread culture missions and then having the city gifted to them... They'd still be paying for the cultural victory, but they'd be paying in espionage rather than in culture. -- So I'm considering changing that, but I don't think it's very important.)
Regarding flaking on panzars. I didn't intend to give them special flanking damage with it. The flanking promotion is a promotion that they've always been allowed to get anyway, and it didn't give them any special flanking damage. The only difference I'm suggesting is that they'd get the promotion for free. I agree that panzars could probably afford to be buffed a lot more than just that without them being too powerful -- but... well... I like to do these things in small steps, for various reasons.
I also like not having my automated move until I want them to.
. I think we need to move back up to Monarch though, that game was a cake walk. Hard to tell sometimes though, with the wrong neighbors the game can be just torturous. 
